Data structure: \(O = (W, A, Y)\)
Underlying data generating process, \(P_{U,X}\)
Outcome of interest: \(E_0[Y|a,W]\)
## W A Y
## Min. :-3.920105 Min. :0.0000 Min. :0.0000
## 1st Qu.:-0.672772 1st Qu.:0.5787 1st Qu.:0.0000
## Median : 0.000686 Median :2.0133 Median :0.0000
## Mean : 0.003438 Mean :2.1197 Mean :0.4689
## 3rd Qu.: 0.676795 3rd Qu.:3.4294 3rd Qu.:1.0000
## Max. : 3.616531 Max. :5.0000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.365 2.753 2.685 4.083 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.8798 2.2863 2.3160 3.6474 5.0000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.4394 1.7482 1.9473 3.1546 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.103 1.516 2.554 5.000
## [1] "The average fitting time for CV-HAL: 4.8179 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 7.3648 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 31.9061 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.003
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.007 0.008 0.023 0.044 0.064 0.108 0.178 0.238 0.351 0.466 0.632
## [1] "The average fitting time for CV-HAL: 5.3619 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 10.0429 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 54.3114 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.000 0.003 0.005 0.016 0.023 0.038 0.059 0.103 0.153 0.221 0.268
## [1] "The average fitting time for CV-HAL: 5.8012 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 11.4634 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 62.6101 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.000 0.001 0.001 0.007 0.010 0.016 0.027 0.047 0.073 0.104 0.135
Data structure: \(O = (W, A, Y)\)
Underlying data generating process, \(P_{U,X}\)
Outcome of interest: \(E_0[Y|a,W]\)
## W A Y
## Min. :-3.61831 Min. :0.000 Min. :0.0000
## 1st Qu.:-0.68682 1st Qu.:0.612 1st Qu.:0.0000
## Median :-0.00980 Median :2.021 Median :0.0000
## Mean :-0.00214 Mean :2.124 Mean :0.0661
## 3rd Qu.: 0.67024 3rd Qu.:3.395 3rd Qu.:0.0000
## Max. : 4.61816 Max. :5.000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.408 2.752 2.694 4.110 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.8729 2.2537 2.3142 3.6316 5.0000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.4784 1.7923 1.9353 3.0472 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.147 1.531 2.612 5.000
## [1] "The average fitting time for CV-HAL: 4.6812 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 6.3512 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 18.9695 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.708 0.720 0.726 0.744 0.769 0.781 0.811 0.827 0.840 0.866 0.888
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.905 0.910 0.926 0.925 0.933 0.934 0.946 0.955 0.960 0.975 0.978
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.946 0.947 0.948 0.944 0.944 0.956 0.969 0.984 0.988 0.990 0.989
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.995 0.995 0.997 1.000 0.999 1.000 1.000 1.000 1.000 1.000 1.000
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.969 0.968 0.971 0.976 0.978 0.989 0.993 0.998 0.999 1.000 1.000
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Data structure: \(O = (W, A, Y)\)
Underlying data generating process, \(P_{U,X}\)
Outcome of interest: \(E_0[Y|a,W]\)
## W A Y
## Min. :-3.61831 Min. :0.000 Min. :0.0000
## 1st Qu.:-0.68682 1st Qu.:0.612 1st Qu.:0.0000
## Median :-0.00980 Median :2.021 Median :0.0000
## Mean :-0.00214 Mean :2.124 Mean :0.4369
## 3rd Qu.: 0.67024 3rd Qu.:3.395 3rd Qu.:1.0000
## Max. : 4.61816 Max. :5.000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.408 2.752 2.694 4.110 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.8729 2.2537 2.3142 3.6316 5.0000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.4784 1.7923 1.9353 3.0472 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.147 1.531 2.612 5.000
## [1] "The average fitting time for CV-HAL: 3.7617 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 6.0892 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 24.4744 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.002 0.003 0.004 0.004 0.008 0.020 0.027 0.049 0.080 0.098 0.132
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.176 0.250 0.300 0.384 0.453 0.549 0.621 0.697 0.762 0.812 0.849
## [1] "The average fitting time for CV-HAL: 5.9994 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 14.4206 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 84.0663 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.005 0.004 0.004 0.004 0.012 0.015 0.022 0.041 0.057 0.074 0.118
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.174 0.243 0.321 0.408 0.510 0.593 0.701 0.794 0.834 0.890 0.916
## [1] "The average fitting time for CV-HAL: 10.6242 seconds"
## [1] "The average fitting time for globally undersmoothed HAL: 22.6256 seconds"
## [1] "The average fitting time for locally undersmoothed HAL: 113.1588 seconds"
## [1] "proportion of simulations that cannot compute empirical SD:"
## 1.2 1.1 1 0.6952 0.4833 0.336 0.2336 0.1624 0.1129 0.0785 0.0546
## 0.000 0.001 0.002 0.005 0.004 0.010 0.013 0.017 0.023 0.044 0.071
## 0.0379 0.0264 0.0183 0.0127 0.0089 0.0062 0.0043 0.003 0.0021 0.0014 0.001
## 0.099 0.149 0.228 0.307 0.396 0.504 0.564 0.640 0.690 0.765 0.787